Question #44108

An aqueous solution at 298 K is prepared by dissolving $0.10$ moles of $\ce{NaHCrO4}$ and $0.09$ moles of the sodium salt of an indicator ($\ce{NaIn}$) in water to make $1.0\text{ L}$ of solution. At equilibrium, the concentration of the dichromate ion, $[\ce{Cr2O7^{2-}}]$, is found to be $0.02\text{ M}$.

Given the following equilibrium constants at 298 K: $2\ce{HCrO4^-} \rightleftharpoons \ce{Cr2O7^{2-}} + \ce{H2O} \quad K_d = 50$ $\ce{HCrO4^-} \rightleftharpoons \ce{H^+} + \ce{CrO4^{2-}} \quad K_a = 4.0 \times 10^{-7}$

Assuming activity coefficients are unity, what is the acid dissociation constant ($K_{In}$) of the indicator $\ce{HIn}$?